SURE-tuned tapering estimation of large covariance matrices

SURE-tuned tapering estimation of large covariance matrices

Bandable covariance matrices are often used to model the dependence structure of variables that follow a nature order. It has been shown that the tapering covariance estimator attains the optimal minimax rates of convergence for estimating large bandable covariance matrices. The estimation risk critically depends on the choice of the tapering parameter.We develop a Stein’s Unbiased Risk Estimat...

Estimation of Large Covariance Matrices

This paper considers estimating a covariance matrix of p variables from n observations by either banding or tapering the sample covariance matrix, or estimating a banded version of the inverse of the covariance. We show that these estimates are consistent in the operator norm as long as (logp)/n→ 0, and obtain explicit rates. The results are uniform over some fairly natural well-conditioned fam...

Covariance Tapering for Likelihood Based Estimation in Large Spatial Datasets

Maximum likelihood is an attractive method of estimating covariance parameters in spatial models based on Gaussian processes. However, calculating the likelihood can be computationally infeasible for large datasets, requiring O(n3) calculations for a dataset with n observations. This article proposes the method of covariance tapering to approximate the likelihood in this setting. In this approa...

Regularized estimation of large covariance matrices

This paper considers estimating a covariance matrix of p variables from n observations by either banding or tapering the sample covariance matrix, or estimating a banded version of the inverse of the covariance. We show that these estimates are consistent in the operator norm as long as (logp)/n→ 0, and obtain explicit rates. The results are uniform over some fairly natural well-conditioned fam...

Minimax Estimation of Large Covariance Matrices 1369